Those 3 bars don't seem to tell you all that much unless I'm just failing to understand.

The Heart is the only one that helps me much as I can see when a fighter is about to go down. But even this one seems to rise and fall randomly throughout the match. For a couple rounds you manage to get your opponents bar down dangerously low and then next round its in good shape.

The other bars move about a little but seem to be pretty stable based on the fighters initial stats.

Don't mistake me; its a fun game. I would just suggest adding to the suspence and excitment by giving a couple more ways to measure your progress in wearing down your opponent.

The heart is the vitality+endurance, and yes, determine if boxer go down.
The fact that goes back up during the game isn't random, but based on what CPU does in the break, and other factors.

Example:
you beat opponent heart (which is endurance) down to 10. During break the CPU choose the strategy to heal the boxer (like the one you can choose too), so that adds a multiplier to the boxer endurance regain (vitality).
What can happen, is that a boxer has endurance 10, but vitality 90, so he gets a huge regain of the endurance, thus the "heart" value goes up again.

Same things happens when he gets knocked down: if manages to get up, regain some endurance. is hard to explain by word, but after trying it, I though that would be cool if a boxer goes back up, filled with "rage", increasing his heart value again, ready to counterattack.

Of course sometime this doesn't happen, like in real boxe, some boxers just go down and if they get up again are a wreck

Yeah... and sometimes they get up when they shouldn't...they have nothing left...and then they get rammed down again with one punch...and get up again... then finally the TKO. The ref should be able to stop those when it's obvious he has nothing left.

Yes, well I don't know if to change that or not. I mean I saw sometime encounters where a boxer wanted to keep fighting but was beaten down, no?
I must admit that is a while (a few years) that I don't watch much boxing on TV, maybe now the referee stops the match more often than before if see the fighter in bad shape?

After a knockdown the ref makes the boxer look at him and he kinda holds up his hands. If his eyes or his legs are too far gone he stops it...not sure how to explain the eyes, but I think you understand.

Yes, and makes sense indeed.
I've added this to the list. It will add a bit of randomness on the game, since referee judgement won't always be "exact" or identic for every situation. In any case if one of your boxers gets beaten so hard, you can't complain for this little bit of randomness in the KO decision!